OFFSET
1,5
LINKS
FORMULA
a(n) = Sum_{i=1..floor(n/2)} i * (1-(floor(n/i)-floor((n-1)/i))).
EXAMPLE
a(10) = 7; the partitions of 10 into two parts are (9,1), (8,2), (7,3), (6,4), (5,5). The sum of the smaller parts that do not divide their larger counterparts is then 3 + 4 = 7.
MATHEMATICA
Table[Sum[i (1 - (Floor[n/i] - Floor[(n - 1)/i])), {i, Floor[n/2]}], {n, 100}]
f[n_] := Plus @@ Select[ Range[n/2], !MemberQ[Divisors[n], #] &]; Array[f, 60] (* Robert G. Wilson v, Dec 23 2017 *)
Table[Total[Select[IntegerPartitions[n, {2}], Mod[#[[1]], #[[2]]]!=0&][[All, 2]]], {n, 60}] (* Harvey P. Dale, Dec 17 2021 *)
PROG
(GAP) List(List(List([1..10^2], n-> Partitions(n, 2)), i -> Filtered(i, j -> j[1] mod j[2] <> 0)), m->Sum(m, k -> k[2])); # Muniru A Asiru, Jan 28 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Dec 23 2017
STATUS
approved